A magnetosonic wave propagating perpendicular to a magnetic field in a two-ion-species plasma has two branches, high-frequency and low-frequency modes. The finite beta effects on these modes are analyzed theoretically on the basis of the three-fluid model with finite ion and electron pressures. First, it is shown that the Korteweg-de Vries (KdV) equation for the low-frequency mode is valid for amplitudes epsilon < epsilon(max), where the upper limit of the amplitude epsilon(max) is given as a function of beta (beta is the ratio of the kinetic and magnetic energy densities), the density ratio, and the cyclotron frequency ratio of two ion species. Next, the linear dispersion relation and KdV equation for the high-frequency mode are derived, including beta as a factor. In addition, the theory for heavy ion acceleration by the high-frequency mode pulse and the pulse damping due to this energy transfer in a finite beta plasma are presented. (C) 2013 AIP Publishing LLC.